X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Frelocation%2Flifts_bind.ma;h=fd56f4e6975b0a5a823b5321adc9d9182042d7dc;hp=0bf6b9fad9a2f561149470c68c450d7bc7ec7d2e;hb=222044da28742b24584549ba86b1805a87def070;hpb=5ea718c8b65a9ca62e8b602800667259b8b2d090

diff --git a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_bind.ma b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_bind.ma
index 0bf6b9fad..fd56f4e69 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_bind.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/relocation/lifts_bind.ma
@@ -12,7 +12,7 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "basic_2/syntax/bind_ext2.ma".
+include "basic_2/syntax/ext2.ma".
 include "basic_2/relocation/lifts.ma".
 
 (* GENERIC RELOCATION FOR BINDERS *******************************************)
@@ -28,37 +28,37 @@ interpretation "generic relocation (binder for local environments)"
 
 (* Basic_inversion lemmas **************************************************)
 
-lemma liftsb_inv_unit_sn: ∀f,I,Z2. ⬆*[f] BUnit I ≡ Z2 → Z2 = BUnit I.
+lemma liftsb_inv_unit_sn: ∀f,I,Z2. ⬆*[f] BUnit I ≘ Z2 → Z2 = BUnit I.
 /2 width=2 by ext2_inv_unit_sn/ qed-.
 
-lemma liftsb_inv_pair_sn: ∀f:rtmap. ∀Z2,I,V1. ⬆*[f] BPair I V1 ≡ Z2 →
-                          ∃∃V2. ⬆*[f] V1 ≡ V2 & Z2 = BPair I V2.
+lemma liftsb_inv_pair_sn: ∀f:rtmap. ∀Z2,I,V1. ⬆*[f] BPair I V1 ≘ Z2 →
+                          ∃∃V2. ⬆*[f] V1 ≘ V2 & Z2 = BPair I V2.
 /2 width=1 by ext2_inv_pair_sn/ qed-.
 
-lemma liftsb_inv_unit_dx: ∀f,I,Z1. ⬆*[f] Z1 ≡ BUnit I → Z1 = BUnit I.
+lemma liftsb_inv_unit_dx: ∀f,I,Z1. ⬆*[f] Z1 ≘ BUnit I → Z1 = BUnit I.
 /2 width=2 by ext2_inv_unit_dx/ qed-.
 
-lemma liftsb_inv_pair_dx: ∀f:rtmap. ∀Z1,I,V2. ⬆*[f] Z1 ≡ BPair I V2 →
-                          ∃∃V1. ⬆*[f] V1 ≡ V2 & Z1 = BPair I V1.
+lemma liftsb_inv_pair_dx: ∀f:rtmap. ∀Z1,I,V2. ⬆*[f] Z1 ≘ BPair I V2 →
+                          ∃∃V1. ⬆*[f] V1 ≘ V2 & Z1 = BPair I V1.
 /2 width=1 by ext2_inv_pair_dx/ qed-.
 
 (* Basic properties *********************************************************)
 
-lemma liftsb_eq_repl_back: ∀I1,I2. eq_repl_back … (λf. ⬆*[f] I1 ≡ I2).
+lemma liftsb_eq_repl_back: ∀I1,I2. eq_repl_back … (λf. ⬆*[f] I1 ≘ I2).
 #I1 #I2 #f1 * -I1 -I2 /3 width=3 by lifts_eq_repl_back, ext2_pair/
 qed-.
 
 lemma liftsb_refl: ∀f. 𝐈⦃f⦄ → reflexive … (liftsb f).
 /3 width=1 by lifts_refl, ext2_refl/ qed.
 
-lemma liftsb_total: ∀I1,f. ∃I2. ⬆*[f] I1 ≡ I2.
+lemma liftsb_total: ∀I1,f. ∃I2. ⬆*[f] I1 ≘ I2.
 * [2: #I #T1 #f elim (lifts_total T1 f) ]
 /3 width=2 by ext2_unit, ext2_pair, ex_intro/
 qed-.
 
-lemma liftsb_split_trans: ∀f,I1,I2. ⬆*[f] I1 ≡ I2 →
-                          ∀f1,f2. f2 ⊚ f1 ≡ f →
-                          ∃∃I. ⬆*[f1] I1 ≡ I & ⬆*[f2] I ≡ I2.
+lemma liftsb_split_trans: ∀f,I1,I2. ⬆*[f] I1 ≘ I2 →
+                          ∀f1,f2. f2 ⊚ f1 ≘ f →
+                          ∃∃I. ⬆*[f1] I1 ≘ I & ⬆*[f2] I ≘ I2.
 #f #I1 #I2 * -I1 -I2 /2 width=3 by ext2_unit, ex2_intro/
 #I #V1 #V2 #HV12 #f1 #f2 #Hf elim (lifts_split_trans … HV12 … Hf) -f
 /3 width=3 by ext2_pair, ex2_intro/
@@ -66,6 +66,6 @@ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma liftsb_fwd_isid: ∀f,I1,I2. ⬆*[f] I1 ≡ I2 → 𝐈⦃f⦄ → I1 = I2.
+lemma liftsb_fwd_isid: ∀f,I1,I2. ⬆*[f] I1 ≘ I2 → 𝐈⦃f⦄ → I1 = I2.
 #f #I1 #I2 * -I1 -I2 /3 width=3 by lifts_fwd_isid, eq_f2/
 qed-.